Implementation of a vector control method requires information about the speed and position of a motor. However, according to a sensorless vector control method, which is employed as a method for acquiring these information items, various information items are estimated without use of any sensors, but rather with use of a magnetic flux estimator.
A related-art induction motor magnetic flux estimator detects stator-side current for at least two phases (e.g., an U-phase current iSU(k) and a V-phase current iSV(k)) and stator-side voltages for at least two phases (e.g., an U-phase voltage VSU(k) and a V-phase voltage iSV(k)) from among an electric current supplied to an induction motor at a point in time of k·Ts second (“k” represents an integer showing a sequence of control steps, and Ts represents the cycle of a control step). Through three-phase to two-phase conversion, the current and voltage are converted into coordinates on an α-β coordinate system of stationary coordinates commonly used for vector control, thereby computing an α-phase current isα(k), a β-phase current isβ(k), an α-phase voltage Vα(k), and a β-phase voltage Vβ(k), which are obtained at time k·Ts second.
A related-art example 1 relates to a magnetic flux estimator equation (1), a speed estimation equation (2), and a phase estimation equation (3), all being derived from an equation of state of an induction motor described in Transactions of the Institute of Electrical Engineers of Japan D, Vol. III, No. 11, pp. 954-960 (1991). Here, an estimated value is given a suffix “est,” thereby indicating that the value is an estimated value.                                                                                                                                     ⅆ                                                                                                                                   ⅆ                      t                                                        ⁡                                      [                                                                                                                        i                                                          s                              ⁢                                                                                                                           ⁢                              α                              ⁢                                                                                                                           ⁢                              est                                                                                                                                                                                                        i                                                          s                              ⁢                                                                                                                           ⁢                              β                              ⁢                                                                                                                           ⁢                              est                                                                                                                                                                                                        ϕ                                                          r                              ⁢                                                                                                                           ⁢                              α                              ⁢                                                                                                                           ⁢                              est                                                                                                                                                                                                                                      ϕ                                                              r                                ⁢                                                                                                                                   ⁢                                β                                ⁢                                                                                                                                   ⁢                                est                                                                                      ⁢                                                                                                                                                                                                       ]                                                  =                                ⁢                                                                            [                                                                                                    ar11                                                                                0                                                                                ar12                                                                                                              -                              ai12                                                                                                                                                            0                                                                                ar11                                                                                ai12                                                                                ar12                                                                                                                                ar21                                                                                0                                                                                ar22                                                                                                              -                              ai22                                                                                                                                                            0                                                                                ar21                                                                                ai22                                                                                ar22                                                                                              ]                                        ⁡                                          [                                                                                                                                  i                                                              s                                ⁢                                                                                                                                   ⁢                                α                                ⁢                                                                                                                                   ⁢                                est                                                                                                           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                                               0                                                                                                                                0                                                                                                              1                                                              σ                                ·                                                                  L                                  s                                                                                                                                                                                                                          0                                                                                0                                                                                                                                0                                                                                0                                                                                              ]                                        ⁡                                          [                                                                                                                                  V                              α                                                                                                                                                                                          V                              β                                                                                                                          ]                                                        +                                                                                                                        ⁢                                                      [                                                                                                                        g                            1                                                                                                                                -                                                          g                              2                                                                                                                                                                                                        g                            2                                                                                                                                g                            1                                                                                                                                                                            g                            3                                                                                                                                -                                                          g                              4                                                                                                                                                                                                        g                            4                                                                                                                                g                            3                                                                                                                ]                                    ⁡                                      [                                                                                                                        i                                                          s                              ⁢                                                                                                                           ⁢                              α                                                                                                                                                            -                                                          i                                                              s                                ⁢                                                                                                                                   ⁢                                α                                ⁢                                                                                                                                   ⁢                                est                                                                                                                                                                                                                                      i                                                          s                              ⁢                                                                                                                           ⁢                              β                                                                                                                                                            -                                                          i                                                              s                                ⁢                                                                                                                                   ⁢                                β                                ⁢                                                                                                                                   ⁢                                est                                                                                                                                                                          ]                                                                                      ⁢                                  ⁢                  Here          ,                                          ⁢                      ar11            =                                          -                                                      R                    s                                                        σ                    ·                                          L                      s                                                                                  -                                                1                  -                  σ                                                  σ                  ·                                      τ                    r                                                                                ,                                           ⁢                      ar12            =                                          -                                  1                  ρ                                            ·                              1                                  τ                  r                                                              ,                                          ⁢                      ai12            =                                                            1                  ρ                                ·                                  ω                  r                                            ⁢                                                           ⁢              or              ⁢                                                           ⁢                                                1                  ρ                                ·                                  ω                  rest                                                                    ⁢                                  ⁢                                                                              ar21                  =                                                            L                      m                                                              τ                      r                                                                      ,                                                                   ⁢                                  ar22                  =                                      -                                          1                                              τ                        r                                                                                            ,                                                                   ⁢                                  ai22                  =                                                            ω                                              r                        ⁢                                                                                                                                         ⁢                    or                    ⁢                                                                                   ⁢                                          ω                      rest                                                                                                                                                                σ                  =                                      1                    -                                                                  L                        m                        2                                                                                              L                          s                                                ·                                                  L                          τ                                                                                                                    ,                                                                   ⁢                                                      τ                    r                                    =                                                            L                      r                                                              R                      r                                                                      ,                                                                   ⁢                                  ρ                  =                                      -                                                                  σ                        ·                                                  L                          s                                                ·                                                  L                          r                                                                                            L                        m                                                                                                                                                    (        1        )            
Rs: resistance of a stator, Rr: resistance of a rotor; Lm: mutual conductance between the rotor and the stator, Ls: self-inductance of the stator, Lr: self-inductance of the rotor, ωr: speed, ωrest: estimated speed, g1, g2, g3, g4: observer feedback gain, isα: α-phase stator current, isβ: β-phase stator current, Vα: α-phase stator voltage, Vβ: β-phase stator voltage, isαest: estimated α-phase stator current, isβest: estimated β-phase stator current, φrαest: estimated α-phase field magnetic flux for a rotor; φrβest: estimated β-phase field magnetic flux for a rotor.ωrest=kωp[φrβest(isα−isαest)−φrαest(isβ−isβest)]  (2)θlest=tan−1(φrβest/φrαest)  (3)
These equations are then developed into a sequential form.                                                                         [                                                                                                                              i                                                      s                            ⁢                                                                                                                   ⁢                            α                            ⁢                                                                                                                   ⁢                            est                                                                          ⁡                                                  (                                                      k                            +                            1                                                    )                                                                                                                                                                                                  i                                                      s                            ⁢                                                                                                                   ⁢                            β                            ⁢                                                                                                                   ⁢                            est                                                                          ⁡                                                  (                                                      k                            +                            1                                                    )                                                                                                                                                                                                  ϕ                                                      r                            ⁢                                                                                                                   ⁢                            α                            ⁢                                                                                                                   ⁢                            est                                                                          ⁡                                                  (                                                      k                            +                            1                                                    )                                                                                                                                                                                                                              ϕ                                                          r                              ⁢                                                                                                                           ⁢                              β                              ⁢                                                                                                                           ⁢                              est                                                                                ⁡                                                      (                                                          k                              +                              1                                                        )                                                                          ⁢                                                                                                                                                                       ]                            =                            ⁢                              [                                                                                                    1                        +                                                  ar11                          ·                                                      T                            s                                                                                                                                      0                                                                                      ar12                        ·                                                  T                          s                                                                                                                                                              -                          ai12                                                ·                                                  T                          s                                                                                                                                                0                                                                                      1                        +                                                  ar11                          ·                                                      T                            s                                                                                                                                                              ai12                        ·                                                  T                          s                                                                                                                                    ar12                        ·                                                  T                          s                                                                                                                                                                        ar21                        ·                                                  T                          s                                                                                                            0                                                                                      1                        +                        ar22                                                                                                                                      -                          ai22                                                ·                                                  T                          s                                                                                                                                                0                                                                                      ar21                        ·                                                  T                          s                                                                                                                                    ai22                        ·                                                  T                          s                                                                                                                                    1                        +                                                  ar22                          ·                                                      T                            s                                                                                                                                              ]                                                                                                      ⁢                                                [                                                                                                                                          i                                                          s                              ⁢                                                                                                                           ⁢                              α                              ⁢                                                                                                                           ⁢                              est                                                                                ⁡                                                      (                            k                            )                                                                                                                                                                                                                    i                                                          s                              ⁢                                                                                                                           ⁢                              β                              ⁢                                                                                                                           ⁢                              est                                                                                ⁡                                                      (                            k                            )                                                                                                                                                                                                                    ϕ                                                          r                              ⁢                                                                                                                           ⁢                              α                              ⁢                                                                                                                           ⁢                              est                                                                                ⁡                                                      (                            k                            )                                                                                                                                                                                                                                                  ϕ                                                              r                                ⁢                                                                                                                                   ⁢                                β                                ⁢                                                                                                                                   ⁢                                est                                                                                      ⁡                                                          (                              k                              )                                                                                ⁢                                                                                                                                                                                       ]                                +                                                      [                                                                                                                                                      1                                                              σ                                ·                                                                  L                                  s                                                                                                                      ·                                                          T                              s                                                                                                                                0                                                                                                                      0                                                                                                                                    1                                                              σ                                ·                                                                  L                                  s                                                                                                                      ·                                                          T                              s                                                                                                                                                                            0                                                                          0                                                                                                                      0                                                                          0                                                                                      ]                                    ⁡                                      [                                                                                                                                                      V                              α                                                        ⁡                                                          (                              k                              )                                                                                                                                                                                                                                      V                              β                                                        ⁡                                                          (                              k                              )                                                                                                                                            ]                                                  +                                                                                                      ⁢                                                [                                                                                                                                          g                            1                                                    ·                                                      T                            s                                                                                                                                                                            -                                                          g                              2                                                                                ·                                                      T                            s                                                                                                                                                                                                                    g                            2                                                    ·                                                      T                            s                                                                                                                                                                            g                            1                                                    ·                                                      T                            s                                                                                                                                                                                                                    g                            3                                                    ·                                                      T                            s                                                                                                                                                                            -                                                          g                              4                                                                                ·                                                      T                            s                                                                                                                                                                                                                    g                            4                                                    ·                                                      T                            s                                                                                                                                                                            g                            3                                                    ·                                                      t                            s                                                                                                                                ]                                ⁡                                  [                                                                                                                                          i                                                          s                              ⁢                                                                                                                           ⁢                              α                                                                                ⁡                                                      (                            k                            )                                                                                                                                                -                                                                                    i                                                              s                                ⁢                                                                                                                                   ⁢                                α                                ⁢                                                                                                                                   ⁢                                est                                                                                      ⁡                                                          (                              k                              )                                                                                                                                                                                                                                                i                                                          s                              ⁢                                                                                                                           ⁢                              β                                                                                ⁡                                                      (                            k                            )                                                                                                                                                -                                                                                    i                                                              s                                ⁢                                                                                                                                   ⁢                                β                                ⁢                                                                                                                                   ⁢                                est                                                                                      ⁡                                                          (                              k                              )                                                                                                                                                            ]                                                                                        (        4        )                                                                                                      ω                  rest                                ⁡                                  (                  k                  )                                            =                            ⁢                                                k                                      ω                    ⁢                                                                                   ⁢                    p                                                  [                                                                                                    ϕ                                                  r                          ⁢                                                                                                           ⁢                          β                          ⁢                                                                                                           ⁢                          est                                                                    ⁡                                              (                        k                        )                                                              ⁢                                          {                                                                                                    i                                                          s                              ⁢                                                                                                                           ⁢                              α                                                                                ⁡                                                      (                            k                            )                                                                          -                                                                              i                                                          s                              ⁢                                                                                                                           ⁢                              α                              ⁢                                                                                                                           ⁢                              est                                                                                ⁡                                                      (                            k                            )                                                                                              }                                                        -                                                                                                                                        ⁢                                                                            ϕ                                              r                        ⁢                                                                                                   ⁢                        α                        ⁢                                                                                                   ⁢                        est                                                              ⁡                                          (                      k                      )                                                        ⁢                                      {                                                                                            i                                                      s                            ⁢                                                                                                                   ⁢                            β                                                                          ⁡                                                  (                          k                          )                                                                    -                                                                        i                                                      s                            ⁢                                                                                                                   ⁢                            β                            ⁢                                                                                                                   ⁢                            est                                                                          ⁡                                                  (                          k                          )                                                                                      }                                                  ]                            +                                                                                        ⁢                                                                    k                                          ω                      ⁢                                                                                           ⁢                      i                                                        ·                                      T                    s                                                  ⁢                                                      ∑                                          i                      =                      0                                        k                                    ⁢                                                                           ⁢                                      [                                                                                                                        ϕ                                                          r                              ⁢                                                                                                                           ⁢                              β                              ⁢                                                                                                                           ⁢                              est                                                                                ⁡                                                      (                            i                            )                                                                          ⁢                                                  {                                                                                                                    i                                sa                                                            ⁡                                                              (                                i                                )                                                                                      -                                                                                          i                                                                  s                                  ⁢                                                                                                                                           ⁢                                  α                                  ⁢                                                                                                                                           ⁢                                  est                                                                                            ⁡                                                              (                                i                                )                                                                                                              }                                                                    -                                                                                                                                                            ⁢                                                                    ϕ                                          r                      ⁢                                                                                           ⁢                      α                      ⁢                                                                                           ⁢                      est                                                        ⁡                                      (                    i                    )                                                  ⁢                                  {                                                                                    i                                                  s                          ⁢                                                                                                           ⁢                          β                                                                    ⁡                                              (                        i                        )                                                              -                                                                  i                                                  s                          ⁢                                                                                                           ⁢                          β                          ⁢                                                                                                           ⁢                          est                                                                    ⁡                                              (                        i                        )                                                                              }                                            ]                                                          (        5        )             θlest=tan−1(φrβest(k)/φrest(k))  (6)
Through use of an observer for an induction motor control circuit which operates in accordance with the above equations, an estimated value of a control step (k+1) is computed from an estimated value or the like of the control step “k.” Specifically, an estimated error between an α-phase estimated current isαest(k), which is estimated by a control loop of the control step “k” at a time of k·Ts second, and an α-phase current isα(k); that is, isα(k)−isαest(k), and an estimated error between a β-phase estimated current isβest(k), which is estimated by the control loop of the control step “k” at a time of k·Ts second, and a β-phase current isβ(k); that is, isβ(k)−isβest(k), are used for computing estimated values isαest(k+1), isβest(k+1), φrαest(k+1), φrβest(k+1) at a time of (k+1)·Ts seconds.
As mentioned above, the related-art example 1 requires a voltage sensor to be used for using the stator-side voltages Vα, Vβ.
Next, a speed sensorless vector control method for an induction motor described in JP-A-7-123798, employed as a related-art 2, is intended for preventing occurrence of impediments to vector control resulting from a “lag” stemming from a course for estimating an actual speed of the induction motor. An actual speed of the induction motor is estimated by means of an identical dimension magnetic flux observer and a speed-adaptive secondary magnetic flux observer formed from a speed-adaptive mechanism. By means of a comparison error signal stemming from comparison between the actual estimated speed and an instruction speed, the current control section is controlled, thereby performing vector control operation. An estimated secondary magnetic flux of the motor determined by the same dimension magnetic flux observer is integrated, thereby determining a corrected slip angular frequency for the motor. Thus, the slip angular frequency instruction value to be used for controlling the current control section is corrected.
A strong desire exists for the related-art induction motor magnetic flux estimator from which the voltage sensor seen in the related-art example 1 is obviated for the sake of cost reduction. As in the case of the related-art 2, a method conceived as one method for implementing cost cutting is to use an α-phase instruction voltage Vα″(k) and a β-phase instruction voltage Vβ″(k) instead of an α-phase measured voltage Vα(k) and a β-phase measured voltage Vβ(k). However, in this case, an error sometimes exists between the voltage instruction value and the actual value. This leads to a problem of occurrence of an error in estimated rotor interlinkage magnetic fluxes φrαest, φrβest and an estimated speed ωrest.
To this end, the invention is aimed at providing a method and device for correcting an estimated speed of a so-called speed sensorless induction motor which can solve drawbacks of the related-art example and does not have any speed sensor capable of accurately estimating a speed.